Application of the theory of hypergraph Laplacian to the multi-agent system

Reference No.	2024c003
Type/Category	Openings at any time-Workshop (II)
Title of Research Project	Application of the theory of hypergraph Laplacian to the multi-agent system
Principal Investigator	Shun Uchida（Oita University, Faculty of Science and Technology・Lecturer）
Research Period	August 21,2024. ～ August 21,2024.
Keyword(s) of Research Fields	Multi-agent system, hypergraph Laplacian, nonlinear evolution equation, subdifferential operator, optimal control problem
Abstract for Research Report	The multi-agent system is a model of network which consists of multiple elements that make decisions autonomously and cooperate to achieve a certain goal through the interaction with each other. We can expect to apply the theory for multi-agent system to various problems, for instance, the control of movements of drones and robots, the optimization of energy supply system, and the mutual communication in sensor networks. Hence many researchers of engineering have recently been interested in this theme. On the other hand, the hypergraph is a mathematical model which consists of a finite number of vertices and small groups of them and describes complex network structures such as the communities on social media and the co-authorship relationships. As for the usual graph (which consists of points and line segments), a method for investigating geometric structures via the graph Laplacian matrix has been established. In recent years, the hypergraph Laplacian has been introduced in order to generalize this theory to a more complicated network. In the previous researches, networks in multi-agent systems are written as the usual graph. Therefore, by generalizing this theory to the hypergraph, we might be able to apply the concept of the multi-agent systems to more complex network structures and various problems in the industrial field. In this workshop, we invite experts in the multi-agent system and the hypergraph Laplacian in order to exchange their and our information on the recent researches and consider each issue from a new point of view.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Shun Uchida（Oita University, Faculty of Science and Technology・Lecturer） Masahiro Ikeda（RIKEN / Keio University, Faculty of Science and Technology・Research Scientist / Visiting researcher）